Athermal optical filter with active tuning and simplified control

ABSTRACT

Embodiments of the invention describe systems, apparatuses and methods for providing athermicity and a tunable spectral response for optical filters. Finite impulse response (FIR) filters are commonly implemented in photonic integrated circuits (PICs) to make devices such as wavelength division multiplexing (WDM) devices, asymmetric Mach-Zehnder interferometers (AMZIs) and array waveguide gratings (AWGs). Athermicity of an FIR filter describes maintaining a consistent frequency transmission spectrum as the ambient temperature changes. A tunable spectral response for an FIR filter describes changing the spectrum of an FIR filter based on its application, as well as potentially correcting for fabrication deviations from the design. In addition, embodiments of the invention reduce energy dissipation requirements and control complexity compared to prior art solutions.

FIELD

Embodiments of the invention generally pertain to optical devices andmore specifically to optical filters.

BACKGROUND

Finite impulse response (FIR) filters are commonly implemented inphotonic integrated circuits (PICs) to make devices such as asymmetricMach-Zehnder interferometers (AMZIs), array waveguide gratings (AWGs),or wavelength division multiplexing (WDM) devices. FIR stages can alsobe assembled in series to make a more complex filter. FIR filter devicesmay be deployed in environments where there can be wide variations inambient temperature, due to both environmental changes and the use ofheat-dissipating components.

FIR filters implemented in PICs have several technical problems. As thematerials used to construct PICs have a temperature-dependent index ofrefraction, temperature changes to FIR filter devices can affect thespectral characteristics of the FIR filter. Correcting for this in adeployed PIC typically requires maintaining the device temperaturewithin a narrow range; this maintenance may require energy-intensiveheating of the entire PIC package.

Furthermore, especially in the case of silicon-on-insulator (SOI) PICs,fabricated devices commonly have deviations from the design which leadto changes in the transmission spectrum. This is because SOI waveguideshave a strong refractive index contrast between the silicon core andsilicon dioxide cladding, and also because of the small dimensionstypical of SOI waveguides; these small dimensions lead the effectiveindex of a mode to be strongly dependent on changes in waveguide crosssectional dimensions. Fabrication deviations may be local, affectingdifferent regions of a PIC to different degrees, or global, causing aconstant deviation of the waveguide cross section from the design. Bothlocal and global deviations detune the spectral response of an FIRfilter.

BRIEF DESCRIPTION OF THE DRAWINGS

The following description includes discussion of figures havingillustrations given by way of example of implementations of embodimentsof the invention. The drawings should be understood by way of example,and not by way of limitation. As used herein, references to one or more“embodiments” are to be understood as describing a particular feature,structure, or characteristic included in at least one implementation ofthe invention. Thus, phrases such as “in one embodiment” or “in analternate embodiment” appearing herein describe various embodiments andimplementations of the invention, and do not necessarily all refer tothe same embodiment. However, they are also not necessarily mutuallyexclusive.

FIG. 1 is an illustration of an athermal optical device according to anembodiment of the invention.

FIG. 2 is an illustration of an athermal optical device utilizing morethan two waveguides according to an embodiment of the invention.

FIG. 3 illustrates two optical devices sharing a common heated regionaccording to an embodiment of the invention.

FIG. 4 is an illustration of an athermal device including a region oflow thermal conductivity according to an embodiment of the invention.

FIG. 5 is an illustration of an optical device for athermal operationand frequency spectrum tuning according to an embodiment of theinvention.

FIG. 6A-FIG. 6C are illustrations of athermal optical devices forfrequency spectrum tuning according to embodiments of the invention.

Descriptions of certain details and implementations follow, including adescription of the figures, which may depict some or all of theembodiments described below, as well as discussing other potentialembodiments or implementations of the inventive concepts presentedherein. An overview of embodiments of the invention is provided below,followed by a more detailed description with reference to the drawings.

DESCRIPTION

Embodiments of the invention describe systems, apparatuses and methodsfor providing athermicity and a tunable spectral response for opticalfilters. Finite impulse response (FIR) filters are commonly implementedin photonic integrated circuits (PICs) to make devices such aswavelength division multiplexing (WDM) devices, asymmetric Mach-Zehnderinterferometers (AMZIs) and array waveguide gratings (AWGs). Athermicityof an FIR filter describes maintaining a consistent frequencytransmission spectrum as the ambient temperature changes. A tunablespectral response for an FIR filter describes changing the spectrum ofan FIR filter based on its application, as well as potentiallycorrecting for fabrication deviations from the design. In addition,embodiments of the invention reduce energy dissipation requirements andcontrol complexity compared to prior art solutions.

In some embodiments of the invention, athermal operation of an FIRfilter on a PIC is obtained via active control by heating a region ofthe filter. A control feedback loop maintains a set point (i.e.,constant) temperature for the heated region; thus, there is no need tosense the ambient temperature or change the heated region's temperatureas a function of the ambient temperature.

By changing the set point temperature, the transmission spectrum of afilter may be linearly shifted to actively tune the filter's response.Shifting the transmission spectrum of a filter may also be used tocorrect for deviations of the fabricated device from the design. In thecase of a global error in fabrication where all waveguides have adifferent effective index from what was designed, the fabricated devicewill have a linear spectral shift from the design intent, whichembodiments of the invention can correct. Because only a fraction of thearea of the device is to be selectively heated, this method of activecontrol is power-efficient.

Embodiments of the invention further describe design features forimproving the power efficiency of a device. In some embodiments, theabove described heated region is thermally isolated from the abovedescribed ambient region through modification of the thermal conductionpath between the heated region and the ambient region, such as throughlocalized thermal engineering of the substrate. In some embodiments,devices are designed to have waveguide regions having differentthermo-optic coefficients (alternatively referred to herein as ‘dn/dT,’as described below), either from differing materials or differingwaveguide cross-sections, wherein a region where waveguides have a highdn/dT is heated, while the remaining bulk of the FIR device useswaveguides with a low dn/dT. Control at the PIC scale can be furthersimplified if an actively heated region is shared by two or more FIRfilter devices.

Throughout this specification, several terms of art are used. Theseterms are to take on their ordinary meaning in the art from which theycome, unless specifically defined herein or the context of their usewould clearly suggest otherwise. In the following description numerousspecific details are set forth to provide a thorough understanding ofthe embodiments. One skilled in the relevant art will recognize,however, that the techniques described herein can be practiced withoutone or more of the specific details, or with other methods, components,materials, etc. In other instances, well-known structures, materials, oroperations are not shown or described in detail to avoid obscuringcertain aspects.

FIG. 1 is an illustration of an athermal optical device according to anembodiment of the invention. Optical device 100 is shown to be an AMZIincluding input ports 102, output ports 104, and multi-mode interference(MMI) couplers 106 and 108. As described herein, a waveguide propagationsection is defined as the region between the input and output portswhere there is more than one waveguide, and the waveguides havedifferent delays/optical path lengths. At the output port (such asoutput ports 104), light from different waveguides in the waveguidepropagation section have undergone interference—for example with an MMI(such as MMIs 106 and 108) or a star coupler.

In this example, waveguides 110 and 112 in the waveguide propagationsection each have differing lengths, wherein waveguide 110 is longerthan waveguide 112. In this example embodiment, the waveguide crosssections do not necessarily vary in the waveguide propagation section;however, other embodiments described below do utilize varying waveguidecross sections in both dimensions and thermo-optic coefficients (dn/dT).In embodiments where different waveguides in the waveguide propagationsection have different deviations in the cross section, said waveguidesare to be heated differently. For example, in embodiments having threeor more waveguides in the waveguide propagation section, the spectrummay be changed in a manner in which different waveguides would be heatedseparately in order to correct their individual phase errors (e.g.,local fabrication errors). In embodiments with only two waveguides inthe waveguide propagation section having different deviations in thecross section, a single heater may be used to shift the spectrum tocorrect the deviation.

In this embodiment, a section of waveguide 110, shown to be included inregion 120, is heated to fixed temperature T_(set) which is greater thanthe ambient temperature of AMZI 100, T_(amb). The region of AMZI 100subjected to the ambient temperature is shown as region 122. The lengthof the waveguide section included in heated region 120 is the differencein lengths between waveguide 110 and waveguide 112. In other words, thelengths of each waveguide which are affected by changes in T_(amb)(shown as length 130) are equal, and the section of waveguide 110included in heated region 120 does not experience any variations inoptical path length with variations in T_(amb). Because the relativephase of modes in different waveguides at the outputs of the waveguidepropagation section does not change with changes to T_(amb), theamplitude transmission characteristic of AMZI 100 is athermal and isthus not restricted to operate within a narrow temperature range as areprior art optical devices.

In one embodiment, region 120 of AMZI 100 represents a boundary linewith low thermal conductivity. The effect of the design of AMZI 100having heated region 120 is to improve power efficiency, increasetemperature uniformity in the T_(set) region, and minimize the heatingof region 122. This may be achieved in a silicon-on-insulator (SOI)platform, for example, by etching a groove in the top silicon to removea thermal conduction path between the T_(set) region and T_(amb) region.Additionally the substrates could be etched to remove thermal conductionpaths.

In another embodiment, the outline of region 120 (i.e., the T_(set)region) may represent the edge of a region of uniformly high thermalconductivity to improve the uniformity of the temperature in the T_(set)region. This may be achieved by depositing a high thermal conductivitymaterial above the top cladding (e.g., replace SiO₂ with diamond), bythinning the cladding or BOX and placing a conductor in close proximityto the waveguide, or by removing the substrate and depositing a highthermal conductivity material below the bottom cladding. In either ofthese implementations the high thermal conductivity material may connectdirectly to the waveguide layer using thermal shunts.

Thus, in this embodiment, athermal operation of an FIR filter in a PICis accomplished by heating a selected area of the filter to a fixedtemperature. AMZI filter 100 (or a single stage thereof) contains awaveguide propagation section with more than one waveguide, and thewaveguides are of different lengths. The waveguide propagation region isselectively heated, so that a given waveguide (i.e., waveguide 110) canbe divided into a fraction that is at the ambient temperature (T_(amb))and a fraction that is at the fixed temperature (T_(set)). The heatedregions are chosen such that each waveguide has an equal length that isat temperature T_(amb), and any remaining length is at T_(set). Theresult is that in response to a fluctuation in T_(amb), each waveguidehas an identical change in the effective optical length, and the outputfrequency spectrum remains unchanged. The size of the heated region canbe very small, making the technique power-efficient. Furthermore, asdescribed in more detail below, varying T_(set) may linearly shift thefrequency spectrum of the filter. This property is useful both tointentionally modify the filter's frequency spectrum and to correct fordeviations between the fabricated device and its pre-fabricated design.

The following description teaches operation of a single stage of an FIRdevice. It is to be understood that the same explanation also applies toa filter of multiple stages, such as an interleaver containing severalcascaded AMZIs. For this description, waveguides in the waveguidepropagation section are referred to numerically as 1, 2 . . . n, and thewaveguide number is a variable ‘w’. The waveguides' lengths are given byL(w). The effective index of the optical mode at position ‘x’ along awaveguide is n_(eff)(w,x). The change in index with change intemperature (dn_(eff)/dT) at position ‘x’ along a waveguide is

$\frac{dn}{dT}{\left( {w,x} \right).}$

An athermal FIR filter may comprise waveguides that are subdivided intoa fixed temperature (i.e., heated) region and an ambient region, asshown in FIG. 1. The fixed temperature region may be hotter than themaximum ambient temperature to ensure device reliability over itsoperating temperature range. It is assumed for the following explanationthat the waveguides all have the same cross section, both in dimensionsand materials, such that:

${{n_{eff}\left( {w,x} \right)} = {constant}},{{\frac{dn}{dT}\left( {w,x} \right)} = {constant}}$

Under these conditions, the heated and ambient regions' lengths sum toequal the total length of the waveguide is:

L _(H)(w)+L _(A)(w)=L(w).

For an AMZI including two waveguides (such as AMZI 100) the heatedregion's length is chosen such that, L(1)−L(2)=L_(H)(1)−L_(H)(2). Ifwaveguide 1 is longer than waveguide 2, then the length of waveguide 1that is heated may be equal to the difference in lengths, and waveguide2 may be completely ambient (e.g., waveguide 112 shown in FIG. 1).

From the previous equation it follows that L_(A)(1)=L_(A)(2). Since thelengths of each waveguide in the waveguide propagation region at theambient temperature are the same, when the ambient temperature changes,the optical path length of each waveguide changes the same amount, andthe differences in length between the waveguides do not change.Therefore, an ambient temperature change may cause a slight time orphase delay in the overall transfer function of the filter but there isno change in the frequency spectrum of the transfer function.

To extend this result to filters with more than two waveguides such asAWGs, fixed temperature lengths L_(H)(w) are chosen such thatL_(A)(n)=L_(A)(1) for any n and 1. FIG. 2 is an illustration of anathermal optical device utilizing more than two waveguides according toan embodiment of the invention.

In this embodiment, FIR device 200 is illustrated as implementing anactive technique to achieve athermicity in an FIR filter with more thantwo waveguides. Device 200 is shown to include two input ports 202 andtwo output ports 204. MMI 210 is coupled to said input ports to achievemode transformation and interference. In other embodiments, MMI 210 maybe replaced by other interferometric components, such as one or moreY-junctions, one or more directional couplers, or a star coupler.

A waveguide propagation section comprising waveguides 221-22 n followsMMI 210, in which the different waveguides have different effectiveoptical path lengths. MMI 212 follows said waveguide propagation sectionto achieve mode transformation and interference; output ports 204 followMMI 212. In other embodiments, MMI 212 could also be replaced withanother interferometric component.

In this embodiment, within said waveguide propagation section, one ormore heaters 250 are used to heat part of the waveguide propagationregion to a fixed temperature T_(set), shown as region 260. The rest ofsaid waveguide propagation section is subject to the surrounding ambienttemperature. The cross section of the waveguide in the ambient region isconstant, and as shown in this illustration, the length of the waveguideregion at the ambient temperature is the same in each of the waveguides.

In this embodiment, heating element 250 comprises a single heatingelement used to heat each of waveguides 221-22 n. This heating elementmay be, for example, a “snake-shaped” thin film resistor that runs alongthe length of several waveguides to be heated. Two potential locationsof resistive thermal device (RTD) 252 for heat sensing are shown in thisillustration. One location is between the traces of the thin filmresistor (i.e., heating element 250). Another location is adjacent tothe resistor but close enough that the temperature at the RTD is veryclose to the temperature of the resistor. Other configurations for boththe heater and RTD can be used in other embodiments of the invention.

It is to be understood that the thermal gradient across device 200 atsteady state is a function of T_(set) and T_(amb). At steady state,provided T_(set)>T_(amb), the temperature at any location in the devicemay be described as a linear combination of T_(amb) and T_(set),satisfying the equation T=a*T_(amb)+b*T_(set), where a+b=1; there is notvariation of the spatial distribution of thermal contours with changesin T_(set) or T_(amb).

Embodiments of the invention further enable a linear shift in thespectrum of the transfer function of the filter by changing temperatureT_(set). The teachings of this description are related to a singlefilter stage but could be applied to a filter with multiple stages. Inaddition, the mathematical analysis describes the response at a singleoutput port to an input in a single input port, but can be extended tosimultaneous inputs to different input ports.

An FIR filter implemented in a PIC may be understood to split and/orinterfere input modes from one or more input ports, propagate severalmodes through different time-delay paths in the waveguide propagationsection, and then combine these modes through interference at one ormore output ports. The transfer function may be described with animpulse response function. This is the response of the system to aninput which is a narrow pulse at time t=0, represented as a deltafunction, δ(t−0). The impulse response function of the filter for inputport k and output port l is:

${h_{k,l}(t)} = {\sum\limits_{w = 1}^{n}\; {c_{k,l,w}{\delta \left( {t - d_{w}} \right)}}}$

The input signal is split into waveguides numbered 1 through n, and thetime delay to propagate through each waveguide is represented by d_(w).When light in different waveguides are combined through interference atthe output, the complex amplitude corresponding to each waveguide isrepresented by c_(k,l,w). Representation of the filter's response as animpulse response function permits a description of the filter'stransmission frequency spectrum. This is found by taking a Fouriertransform of h_(k,l)(t), which will be written as H_(k,l)(ω).Representation of the transmission frequency spectrum in this waypermits a mathematical description of how changing the heating profileof the waveguides changes the spectrum.

The delay times d_(w) are proportional to the effective path lengths ofthe waveguides. Since the effective ambient length of each waveguide isthe same and the effective heated length of each waveguide is different,if the fixed temperature T_(set) is changed, the new delay time (g_(w))changes by an amount proportional to the total path delay minus aconstant delay time, d₀, which is identical for each waveguide andcorresponds to the unheated ambient length of each path. Mathematicallythis may be described by the following equation where the factor sequals 1 when there is no change in T_(set), but has a different valuewhen temperature is changed:

g _(w) =s*(d _(w) −d ₀)+d ₀

The frequency spectrum after change in T_(set) may be expressed in termsof H_(k,l)(ω) using the well-known Fourier transform properties, shownhere for a function in time f(t) and its Fourier transform F(w):

Time shift property: f(t−t₀) corresponds to F(ω)e^(−jωt) ⁰

Scaling property for real a: f(a*t) corresponds to

$\frac{1}{|a|}{F\left( \frac{\omega}{a} \right)}$

Applying these properties, the frequency spectrum of the transferfunction after change in T_(set) is:

$\frac{1}{|s|}{H_{k,l}\left( \frac{\omega}{s} \right)}e^{j\; \omega \; {t_{0}{({1 - \frac{1}{s}})}}}$

The amplitude of this function is:

$\left| \frac{H_{k,l}\left( \frac{\omega}{s} \right)}{s} \right|$

This function represents a scaling in the width of the entire frequencyspectrum. Because the shift in center frequency is small compared to thecarrier frequency, this spectral shift may typically beindistinguishable from a linear shift of the entire frequency spectrum,in the wavelength range of interest.

FIG. 3 illustrates two optical devices sharing a common heated regionaccording to an embodiment of the invention. In this embodiment, device300 includes MMI 302 and 304, coupled via waveguide propagation section306; device 310 includes MMI 312 and 314, coupled via waveguides 316 and318.

In this embodiment, sections of waveguide propagation section 306 areheated in a manner similar to the example embodiment of FIG. 2 (i.e.,wherein the waveguides of waveguide propagation section 306 havevariable section lengths to be heated, and equal section lengths subjectto the ambient temperature). Waveguide 316 includes a portion to beheated to a constant temperature, similar to the embodiment of FIG. 1.As shown in this illustration, devices 300 and 310 both utilize region350, which is heated to a constant temperature (i.e., greater than theambient temperature).

The heating of region 350 may be accomplished by using a single thinfilm electrode that covers the length of all of the waveguides withinsaid region. In other embodiments, said constant temperature region maybe implemented with the use of regions of high and/or low thermalconductivity to make the temperature in the T_(set) region uniform,thereby avoiding heating the T_(amb) region and improving powerefficiency. This implementation allows the heater, RTD, heater drivercircuit, and feedback control circuit to be shared between two or moreFIR filter devices or stages in an FIR filter.

FIG. 4 is an illustration of an athermal device including a region oflow thermal conductivity according to an embodiment of the invention. Inthis embodiment, device 400 includes input port 402 and output port 404coupled via waveguides 406. Device 400 utilizes heater 410 set at afixed temperature to achieve athermal behavior. A region of low thermalconductivity, shown as region 412, is used to control the thermalgradient between heater 410 and the ambient region (i.e., the regionoutside of region 412).

The low thermal conductivity of region 412 may be achieved, for example,by etching away the waveguide slab region between waveguides.Additionally a thermally conductive substrate may be removed in thisregion. The direction of the generated thermal gradient (shown in thisexample by directional arrow 414) corresponds to a change in temperaturewith distance that is roughly linear.

The following description teaches the athermicity condition moregenerally where there is a thermal gradient in the vicinity of theheater, but the waveguides still have an invariant cross section.Assuming the thermal gradients are solely due to interaction of twothermal bodies—a heat sink held at the ambient temperature and theheater, and further assuming the temperature has reached steady state,the temperature at any location in the device may be described as alinear combination of the ambient and the fixed temperature. Temperatureat a location along a waveguide may be expressed as:

T(w,x)=a(w,x)*T _(amb) +b(w,x)*T _(set)

a(w,x) is the fractional weight of the ambient temperature, and b(w,x)is the fractional weight of the set temperature. Both of these functionsare temperature-invariant: They do not change as T_(amb) or T_(set)change. At all locations, a(w,x)+b(w,x)=1.

A waveguide may thus be described as being subdivided into effectivelengths that are at the fixed and ambient temperatures, which may bedifferent from the lengths which are and are not covered by a heatingelement:

L _(A)(w)=∫₀ ^(L(w)) a(w,x)*dx

L _(H)(w)=∫₀ ^(L(w)) b(w,x)*dx

Therefore the effective length of each waveguide that is heated to theheater temperature may change by a constant length between each adjacentwaveguide, allowing the condition for athermicity to be satisfied. Thisembodiment demonstrates that not only can the shape of the heater orheated region be designed to heat different lengths of each waveguide inan FIR filter, but the thermal gradient can also be engineered so thatthe effective length of the heated region of each waveguide is correctto achieve athermal behavior.

The condition to be satisfied for athermicity in this case is also:L_(A)(k)=L_(A)(l) for any k and l. This method embodiment works in thepresence of a thermal gradient since the waveguide can be subdividedinto an effective length at the ambient temperature and an effectivelength at the heated temperature, and because these effective lengths donot change as a function of the ambient and fixed temperatures.

PICs according to embodiments of the invention, may also utilizepassively athermal FIR filters using waveguide regions with differenteffective thermo-optic coefficients do/dT and heating a selected area ofthe PIC. By changing the power dissipated by the localized heater, thefrequency spectrum of the FIR filter linearly shifts, despite itsathermicity, in the presence of global ambient temperature changes.Shifting the frequency spectrum can accomplish both active tuning of thefilter characteristic and correction of deviations of the fabricateddevice from design. Using this technique, neither monitoring oftemperatures on the chip nor feedback during heater operation isnecessary.

FIG. 5 is an illustration of an optical device for athermal operationand frequency spectrum tuning according to an embodiment of theinvention. In this embodiment, device 500 includes MMI 502 and MMI 504,coupled via waveguides 510 and 520; said waveguides comprise more thanone value of dn/dT, either through differing materials or differingwaveguide dimensions. If a heater is used for active tuning, constantpower dissipation may be used such that the heated region is raised toT_(amb)+T_(off), where T_(off) is a function of heater powerdissipation. Measurement of temperatures on the chip may not necessaryfor this embodiment; said active tuning can be used to compensate forfabrication variations or to intentionally shift the spectrum of device500.

In this embodiment, one of either waveguide sections 512 or 522comprises a region having a differing dn/dT value, either throughdiffering materials or differing waveguide dimensions, compared to therest of waveguides 510 or 520, respectively. One of either waveguidesections 512 or 522 may also function as an active tuning sectionthrough the use of a heater. For example, waveguide section 512 maycomprise a region having a higher dn/dT value compared to the rest ofwaveguide 510 while waveguide section 522 comprises a heater, orvice-versa. In other embodiments, waveguide section 512 may comprise aboth a region having a higher dn/dT value compared to the rest ofwaveguide 510 and a heater either overlapping or in sequence with saidwaveguide section (e.g., said high dn/dT region and said heater areplaced in series), while waveguide section 522 comprises a normalwaveguide (i.e., a passive waveguide comprising the same dn/dT value asthe “low” dn/dT region of waveguide 510), or vice-versa.

Thus, embodiments of the invention may further utilize passivelyathermal FIR filters having waveguide regions with different values ofdn_(eff)/dT in combination with heating a selected area of the device.Changing the power dissipated by the localized heater linearly shiftsthe frequency spectrum of the FIR filter, despite its athermal design(i.e., athermicity in the presence of global ambient temperature changesdue to the varying dn_(eff)/dT materials used). Shifting the frequencyspectrum can accomplish both active tuning of the filter characteristicand correction of deviations of the fabricated device from design. Usingthis technique, neither monitoring of temperatures on the chip norfeedback during heater operation is necessary: the heated region'stemperature is a sum of the ambient temperature and an offsettemperature that is a linear function of power dissipated by the heater:T_(heated)=T_(amb)+T+_(off).

The shift of the frequency spectrum is determined by the offsettemperature, which may be set without the need for feedback, as it isproportional to the power dissipated in the heater. Since resistance ofthe heater does not vary strongly with temperature, the heater setpointmay be set with a constant current or constant voltage source. Thistechnique may reduce power dissipation in comparison to the previouslydescribed embodiments, as heating is not required to achieve athermaloperation but only to shift the frequency spectrum of the device. Someembodiments of the invention are further configured to heat a regionwithin the high dn/dT waveguide cross section to maximize the energyefficiency of tuning.

For passive athermal operation, an FIR filter may use waveguide crosssections with differing effective thermo-optic coefficients (dn/dT).Each waveguide's length L(w) may be subdivided into lengths with the twodifferent values of dn/dT:

L(w)=L ₁(w)+L ₂(w)

The net change in optical length with temperature is the same for allwaveguides:

${{\frac{{dn}_{1}}{dT}*{L_{1}(w)}} + {\frac{{dn}_{2}}{dT}*{L_{2}(w)}}} = {constant}$

The result is analogous to the effect of the previously describedembodiments utilizing a heater to heat a portion of an optical device toa fixed temperature—when the ambient temperature is changed, theeffective optical path length of each waveguide is changed by a fixedamount. The differences in effective optical path lengths betweendifferent waveguides are invariant with temperature. A change is ambienttemperature may therefore result in a small time/phase delay, but nochange in the transmission frequency spectrum.

This relation may also be stated in integral form, which is applicablefor embodiments with free variation of do/dT along the waveguides'length instead of two discrete cross sections:

${\int_{0}^{L{(w)}}{\frac{dn}{dT}\left( {w,x} \right)*{dx}}} = {constant}$

Using the above described passive athermal design, embodiments of theinvention may further use a heater to heat a region of the waveguidepropagation section for frequency spectrum tuning. The temperature ofsaid heated region is T_(amb)+T_(off). The thermal gradient in thevicinity of the heater may be described by b(w,x), where 0<b(w,x)≤1. Thetemperature at any point along a waveguide may be described by:

T(w,x)=T _(amb) +T _(off) *b(w,x)

The shape of the heated region may chosen such that:

${\int_{0}^{L{(w)}}{\frac{dn}{dT}\left( {w,x} \right)*{b\left( {w,x} \right)}*{dx}}} = {{u*{\int_{0}^{L{(w)}}{{n_{eff}\left( {w,x} \right)}*{dx}}}} + v}$

For an optical device with two waveguides in its waveguide propagationsection, the equation may be satisfied by any combination ofheaters—e.g., a single heater of any length on one of the twowaveguides. For an optical device where the effective length differencein adjacent waveguides has a constant linear increment, the length ofthe heated region between adjacent waveguides may also have a constantlinear increment. The heated region can therefore be wedge-shaped asshown in FIG. 6A-6C and described in further detail below.

When the offset temperature is changed, the relative changes in pathlengths causes a linear shift in the transmission frequency spectrum ofthe FIR filter, as explained by the following equations.

The delay time of a waveguide when T_(off)=0 expressed in terms of thespeed of light, c, is:

${{d\left( {w,0} \right)} = {\frac{1}{c}*{\int_{0}^{L{(w)}}{{n_{eff}\left( {w,x} \right)}*{dx}}}}}\ $

When the heater is used the delay time changes to:

${d\left( {w,T_{off}} \right)} = {\frac{1}{c}*\left( {{\left( {1 + {u*T_{off}}} \right)*{\int_{0}^{L{(w)}}{{n_{eff}\left( {w,x} \right)}*{dx}}}} + {v*T_{off}}} \right)}$d(w, T_(off)) = d(w, 0) * (1 + u * T_(off)) + v * T_(off)

The following variable substitutions may be made:

$u = \frac{s - 1}{T_{off}}$ $v = {\frac{1 - s}{T_{off}}*d_{0}}$

Now the equation for d(w,T_(off)) matches the form of the equation forwaveguide delay with temperature shift from the previous section,g_(w)=s*(d_(w)−d₀)+d₀. Therefore, using the math in the previoussection, if the unheated frequency spectrum of the transfer function isfrom input port k to output port l is:

H _(k,l)(ω)

Once the heater temperature is heated to an offset from the ambienttemperature of T_(off), the magnitude of the frequency spectrum is:

$\left| \frac{H_{k,l}\left( \frac{\omega}{1 + {u*T_{off}}} \right)}{1 + {u*T_{off}}} \right|$

This function represents a scaling in the width of the entire frequencyspectrum. As the shift in spectrum is entirely a function of thetemperature offset from ambient and not a function of the ambienttemperature, control of the transmission spectrum of the filter may beachieved without feedback.

FIG. 6A-FIG. 6C are illustrations of athermal optical devices forfrequency spectrum tuning according to embodiments of the invention.These embodiments describe PICs utilizing heating elements incombination with athermal FIR filters using waveguide regions withdifferent values of dn_(eff)/dT. FIG. 6A illustrates device 600 havinginput port 602 and output ports 604 coupled via plurality of waveguides610. In this embodiment, waveguides 610 are comprised two waveguidesegment regions—low dn/dT region 612 and high dn/dT region 614, which isshown to include heated region 616. The waveguide segments of region 614are also shown to be shorter in length than the waveguide segments ofregion 612.

Said heated region's temperature is the sum of the ambient temperatureand an offset temperature that is a linear function of power dissipatedby the heater: T_(heated)=T_(amb)+T_(off). The shift of the frequencyspectrum is determined by the offset temperature, which may be setwithout the need for feedback, since it is proportional to the powerdissipated in the heater. Since resistance of the heater does not varystrongly with temperature, the heater setpoint may be set with aconstant current or constant voltage source. This technique may reducepower dissipation in comparison to the previously described embodimentsas heating is not required to achieve athermal operation but only toshift the frequency spectrum of the device. Heating a region within highdn/dT region 614 may also maximize the energy efficiency of tuning.

For embodiments of the invention having thermo-optic coefficients(dn/dT) due to changes in the waveguide cross section, the athermicitycondition may be stated as the equality between the change in opticalpath lengths per unit change in temperature for different waveguides.The change in optical path length of a waveguide per change in ambienttemperature may be expressed as:

${D(w)} = {\int_{0}^{L{(w)}}{\frac{dn}{dT}\left( {w,x} \right)*{a\left( {w,x} \right)}*{dx}}}$

The condition to be satisfied is D(k)=D(l) for any k and l. Theimplication of the equation is that for a change in ambient temperaturedT, the change in optical path length in each path in the waveguidepropagation region is the same. This is analogous to the previousequation L_(A)(1)=L_(A)(2), except that this more general descriptionallows for variations in both n_(eff) and dn/dT, and also allows for adesign with arbitrary thermal gradients between the heated and ambientregion expressed by a(w,x).

Thus embodiments of the invention include optical devices that utilizemultiple dn/dT regions to decrease the power required to heat the abovedescribed T_(set) region. FIG. 6A shows an AWG using regions with morethan one waveguide cross section. The waveguide types may differ inrefractive index n and in dn/dT. By using a region with a lower dn/dTfor the majority of the waveguide propagation section (i.e., region612), the total phase change along a waveguide with change intemperature is reduced. By using a region with higher dn/dT for theT_(set) region (i.e., region 616), a smaller region needs to be heatedto compensate for changes in T_(amb). The length that is to be heated isreduced by a factor of (dn/dT)_(high)/(dn/dT)_(low) compared to thelength that would be heated if the entire device were made from thewaveguide cross section with (dn/dT)_(low).

FIG. 6B illustrates device 620 having input port 622 and output ports624 coupled via plurality of waveguides 630. In this embodiment,waveguides 630 are materials having different thermo-optic coefficients(dn/dT); as shown in this illustration, a wedge-shaped region in themiddle of device 620, shown as region 632, has a lower dn/dT value thanthe rest of the waveguide propagation region. The shape of region 632 ischosen to fulfill the condition for passive athermicity. Thus, thedesign of region 632 provides athermicity to device 620. In thisembodiment, a heater (region 634) is disposed in or near the higherdn/dT region to improve the energy-efficiency of any desired spectraltuning.

FIG. 6C illustrates another variant of a passively athermal opticaldevice with active tuning. Device 640 is shown as having input port 642and output ports 644 coupled via plurality of waveguides 650. In thisembodiment, wedge-shaped region 652 includes segments of waveguides 650that have a higher dn/dT value than the rest of the waveguide segmentsof propagation region 650. In this embodiment, the heated region iscoincident with high dn/dT wedge-shaped region 652 so the spectraltuning may be energy-efficient. The wedge shape is defined by thepassive athermicity condition where the relative lengths of thewaveguides with differing dn/dT are chosen to maintain a relative phasedifference between adjacent waveguides with temperature fluctuation.

Reference throughout the foregoing specification to “one embodiment” or“an embodiment” means that a particular feature, structure orcharacteristic described in connection with the embodiment is includedin at least one embodiment of the present invention. Thus, appearancesof the phrases “in one embodiment” or “in an embodiment” in variousplaces throughout the specification are not necessarily all referring tothe same embodiment. Furthermore, the particular features, structures orcharacteristics may be combined in any suitable manner in one or moreembodiments. In addition, it is appreciated that the figures providedare for explanation purposes to persons ordinarily skilled in the artand that the drawings are not necessarily drawn to scale. It is to beunderstood that the various regions, layers and structures of figuresmay vary in size and dimensions.

The above described embodiments of the invention may comprise SOI orsilicon based (e.g., silicon nitride (SiN)) devices, or may comprisedevices formed from both silicon and a non-silicon material. Saidnon-silicon material (alternatively referred to as “heterogeneousmaterial”) may comprise one of III-V material, magneto-optic material,or crystal substrate material.

III-V semiconductors have elements that are found in group III and groupV of the periodic table (e.g., Indium Gallium Arsenide Phosphide(InGaAsP), Gallium Indium Arsenide Nitride (GaInAsN)). The carrierdispersion effects of III-V based materials may be significantly higherthan in silicon based materials, as electron speed in III-Vsemiconductors is much faster than that in silicon. In addition, III-Vmaterials have a direct bandgap which enables efficient creation oflight from electrical pumping. Thus, III-V semiconductor materialsenable photonic operations with an increased efficiency over silicon forboth generating light and modulating the refractive index of light.

Thus, III-V semiconductor materials enable photonic operation with anincreased efficiency at generating light from electricity and convertinglight back into electricity. The low optical loss and high qualityoxides of silicon are thus combined with the electro-optic efficiency ofIII-V semiconductors in the heterogeneous optical devices describedbelow; in embodiments of the invention, said heterogeneous devicesutilize low loss heterogeneous optical waveguide transitions between thedevices' heterogeneous and silicon-only waveguides.

Magneto-optic materials allow heterogeneous PICs to operate based on themagneto-optic (MO) effect. Such devices may devices utilize the FaradayEffect, in which the magnetic field associated with an electrical signalmodulates an optical beam, offering high bandwidth modulation, androtates the electric field of the optical mode enabling opticalisolators. Said magneto-optic materials may comprise, for example,materials such as such as iron, cobalt, or yttrium iron garnet (YIG).

Crystal substrate materials provide heterogeneous PICs with a highelectro-mechanical coupling linear electro optic coefficient, lowtransmission loss, and stable physical and chemical properties. Saidcrystal substrate materials may comprise, for example, lithium niobate(LiNbO3) or lithium tantalate (LiTaO3).

In the foregoing detailed description, the method and apparatus of thepresent invention have been described with reference to specificexemplary embodiments thereof. It will, however, be evident that variousmodifications and changes may be made thereto without departing from thebroader spirit and scope of the present invention. The presentspecification and figures are accordingly to be regarded as illustrativerather than restrictive.

1. (canceled)
 2. A tunable optical filter, comprising: a first waveguideincluding a first waveguide section and a second waveguide section, thesecond waveguide section having a higher temperature coefficient ofrefractive index than the first waveguide section; a second waveguide;an input coupler to split incident light into the first and secondwaveguides; an output coupler to interfere light from the first andsecond waveguides to produce interfered light; a heater to heat at leasta portion of the second waveguide section; and a temperature controllerto control the heater to tune a frequency spectrum of the interferedlight.
 3. The tunable optical filter of claim 2, wherein the temperaturecoefficient of refractive index represents a change in refractive indexwith respect to temperature.
 4. The tunable optical filter of claim 2,wherein: a material of the first waveguide section includes a firstmaterial having a first thermal conductivity; and a material of thesecond waveguide section includes a second material having a secondthermal conductivity greater than the first thermal conductivity.
 5. Thetunable optical filter of claim 2, wherein a width of the secondwaveguide section is greater than a width of the first waveguidesection.
 6. The tunable optical filter of claim 2, wherein thetemperature controller is configured to tune the frequency spectrum atleast in part in response to an amount of power dissipated by theheater.
 7. The tunable optical filter of claim 2, further comprising atemperature sensor configured to sense a temperature of the portion ofthe second waveguide section, and wherein the temperature controller isconfigured to tune the frequency spectrum at least in part in responseto the sensed temperature.
 8. The tunable optical filter of claim 2,wherein: the first waveguide section has a first length; and the secondwaveguide section has a second length greater than the first length. 9.The tunable optical filter of claim 2, wherein: the first waveguidesection has a first length; and the second waveguide section has asecond length less than the first length.
 10. The tunable optical filterof claim 2, wherein: the first waveguide section has a first length anda first temperature coefficient of refractive index; the secondwaveguide section has a second length and a second temperaturecoefficient of refractive index greater than the first temperaturecoefficient of refractive index; the second waveguide includes a thirdwaveguide section and a fourth waveguide section; the third waveguidesection has a third length and a third temperature coefficient ofrefractive index; the fourth waveguide section has a fourth length and afourth temperature coefficient of refractive index greater than thethird temperature coefficient of refractive index; and a product of thefirst length and the first temperature coefficient of refractive indexadded to a product of the second length and the second temperaturecoefficient of refractive index differs from a product of the thirdlength and the third temperature coefficient of refractive index addedto a product of the fourth length and the fourth temperature coefficientof refractive index.
 11. A method for tuning a tunable optical filter,the method comprising: splitting incident light into first and secondwaveguides, the first waveguide including a first waveguide section anda second waveguide section, the second waveguide section having a highertemperature coefficient of refractive index than the first waveguidesection; interfering light from the first and second waveguides toproduce interfered light; heating at least a portion of the secondwaveguide section with a heater; and controlling the heater with atemperature controller to tune a frequency spectrum of the interferedlight.
 12. The method of claim 11, wherein: a material of the firstwaveguide section includes a first material having a first thermalconductivity; and a material of the second waveguide section includes asecond material having a second thermal conductivity greater than thefirst thermal conductivity.
 13. The method of claim 11, wherein a widthof the second waveguide section is greater than a width of the firstwaveguide section.
 14. The method of claim 11, wherein the temperaturecontroller is configured to tune the frequency spectrum at least in partin response to an amount of power dissipated by the heater.
 15. Themethod of claim 11, further comprising a temperature sensor configuredto sense a temperature of the portion of the second waveguide section,and wherein the temperature controller is configured to tune thefrequency spectrum at least in part in response to the sensedtemperature.
 16. The method of claim 11, wherein: the first waveguidesection has a first length; and the second waveguide section has asecond length different from the first length.
 17. Atemperature-stabilized optical filter, comprising: a first waveguideincluding a first waveguide section and a second waveguide section, thefirst waveguide section having a first length and a first temperaturecoefficient of refractive index, the second waveguide section having asecond length and a second temperature coefficient of refractive indexgreater than the first temperature coefficient of refractive index; asecond waveguide including a third waveguide section and a fourthwaveguide section, the third waveguide section having a third length anda third temperature coefficient of refractive index, the fourthwaveguide section having a fourth length and a fourth temperaturecoefficient of refractive index greater than the third temperaturecoefficient of refractive index, wherein a product of the first lengthand the first temperature coefficient of refractive index added to aproduct of the second length and the second temperature coefficient ofrefractive index equals a product of the third length and the thirdtemperature coefficient of refractive index added to a product of thefourth length and the fourth temperature coefficient of refractiveindex; an input coupler to split incident light into the first andsecond waveguides; an output coupler to interfere light from the firstand second waveguides to produce interfered light; a heater to heat atleak a portion of the second and fourth waveguide sections; and atemperature controller to control the heater to heat the portion of thesecond and fourth waveguide sections to a fixed temperature and therebystabilize a frequency spectrum of the interfered light.
 18. Thetemperature-stabilized optical filter of claim 17, wherein: a materialof the first and third waveguide sections includes a first materialhaving a first thermal conductivity; and a material of the second andfourth waveguide sections includes a second material having a secondthermal conductivity greater than the first thermal conductivity. 19.The temperature-stabilized optical filter of claim 17, wherein: a widthof the second waveguide section is greater than a width of the firstwaveguide section; and a width of the fourth waveguide section isgreater than a width of the third waveguide section.
 20. Thetemperature-stabilized optical filter of claim 17, wherein thetemperature controller is configured to control the heater at least inpart in response to an amount of power dissipated by the heater.
 21. Thetemperature-stabilized optical filter of claim 17, further comprising atemperature sensor configured to sense a temperature of the portion ofthe second waveguide section, and wherein the temperature controller isconfigured to control the heater at least in part in response to thesensed temperature.